Finally, you may be puzzled how one can tell class 1 and class 2 apart.

There are some hints:

Некоторый and несколько are always class 1 (indefinite).

Некто and нечто are class 1 (indefinite) when they are used in their dictionary form.
They are class 2 (lack of ability) when they are used in any oblique case (other than the dictionary form): некого (нечего), некому (нечему), некем (нечем), не о ком (не о чем).
All the examples are in my posts above.

Некогда is really ambiguous. It can mean "once upon a time", and it can mean "there is no time for someone to do something". The difference can be only deducted from the context:
Некогда Москва была маленьким городом. - Once upon a time Moscow was a small town.
В Москве отдыхать некогда. - There is no time to have a rest in Moscow.
The first usage is however outdated.

I think, all other pronouns with "не-" are only "lack of ability".


And yes, Mr Smith!
If you feel you don't fully understand something, don't get upset! I would say (it's my personal opinion) that the indefinite pronouns (не-, кое-, -то, -либо, -нибудь) is one of the most complicated things in Russian grammar. And the pronouns with "не-" are the most complicated even among the other indefinite pronouns.
So, you have found a very nice (jokingly) question to ask about
As to my opinion, I would not recommend to the beginners to be bothered with "не-" pronouns too much. They are more for advanced level. (That does not apply to the negative "ни-" pronouns, they are much easier). The main thing you should remember is that "не-" pronouns are not like "ни-" ones! They are a completely different continent, and pronounced differently.